'Total return, when measuring performance, is the actual rate of return of an investment or a pool of investments over a given evaluation period. Total return includes interest, capital gains, dividends and distributions realized over a given period of time. Total return accounts for two categories of return: income including interest paid by fixed-income investments, distributions or dividends and capital appreciation, representing the change in the market price of an asset.'

Which means for our asset as example:- Compared with the benchmark SPY (81.9%) in the period of the last 5 years, the total return, or increase in value of 105.2% of ProShares Ultra Dow30 is larger, thus better.
- Looking at total return in of 37.5% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (46.1%).

'The compound annual growth rate (CAGR) is a useful measure of growth over multiple time periods. It can be thought of as the growth rate that gets you from the initial investment value to the ending investment value if you assume that the investment has been compounding over the time period.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (12.7%) in the period of the last 5 years, the annual return (CAGR) of 15.5% of ProShares Ultra Dow30 is greater, thus better.
- Looking at compounded annual growth rate (CAGR) in of 11.2% in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (13.5%).

'Volatility is a statistical measure of the dispersion of returns for a given security or market index. Volatility can either be measured by using the standard deviation or variance between returns from that same security or market index. Commonly, the higher the volatility, the riskier the security. In the securities markets, volatility is often associated with big swings in either direction. For example, when the stock market rises and falls more than one percent over a sustained period of time, it is called a 'volatile' market.'

Using this definition on our asset we see for example:- Compared with the benchmark SPY (19.8%) in the period of the last 5 years, the 30 days standard deviation of 40.6% of ProShares Ultra Dow30 is greater, thus worse.
- During the last 3 years, the 30 days standard deviation is 47%, which is higher, thus worse than the value of 23% from the benchmark.

'Downside risk is the financial risk associated with losses. That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure) measures both the upside and downside risk. Specifically, downside risk in our definition is the semi-deviation, that is the standard deviation of all negative returns.'

Which means for our asset as example:- The downside volatility over 5 years of ProShares Ultra Dow30 is 29.6%, which is larger, thus worse compared to the benchmark SPY (14.5%) in the same period.
- During the last 3 years, the downside risk is 34.1%, which is higher, thus worse than the value of 16.8% from the benchmark.

'The Sharpe ratio was developed by Nobel laureate William F. Sharpe, and is used to help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk. Subtracting the risk-free rate from the mean return allows an investor to better isolate the profits associated with risk-taking activities. One intuition of this calculation is that a portfolio engaging in 'zero risk' investments, such as the purchase of U.S. Treasury bills (for which the expected return is the risk-free rate), has a Sharpe ratio of exactly zero. Generally, the greater the value of the Sharpe ratio, the more attractive the risk-adjusted return.'

Which means for our asset as example:- Looking at the risk / return profile (Sharpe) of 0.32 in the last 5 years of ProShares Ultra Dow30, we see it is relatively smaller, thus worse in comparison to the benchmark SPY (0.52)
- During the last 3 years, the Sharpe Ratio is 0.18, which is lower, thus worse than the value of 0.48 from the benchmark.

'The Sortino ratio, a variation of the Sharpe ratio only factors in the downside, or negative volatility, rather than the total volatility used in calculating the Sharpe ratio. The theory behind the Sortino variation is that upside volatility is a plus for the investment, and it, therefore, should not be included in the risk calculation. Therefore, the Sortino ratio takes upside volatility out of the equation and uses only the downside standard deviation in its calculation instead of the total standard deviation that is used in calculating the Sharpe ratio.'

Which means for our asset as example:- Looking at the ratio of annual return and downside deviation of 0.44 in the last 5 years of ProShares Ultra Dow30, we see it is relatively lower, thus worse in comparison to the benchmark SPY (0.7)
- Compared with SPY (0.65) in the period of the last 3 years, the downside risk / excess return profile of 0.25 is smaller, thus worse.

'The ulcer index is a stock market risk measure or technical analysis indicator devised by Peter Martin in 1987, and published by him and Byron McCann in their 1989 book The Investors Guide to Fidelity Funds. It's designed as a measure of volatility, but only volatility in the downward direction, i.e. the amount of drawdown or retracement occurring over a period. Other volatility measures like standard deviation treat up and down movement equally, but a trader doesn't mind upward movement, it's the downside that causes stress and stomach ulcers that the index's name suggests.'

Using this definition on our asset we see for example:- The Ulcer Ratio over 5 years of ProShares Ultra Dow30 is 15 , which is higher, thus worse compared to the benchmark SPY (6.08 ) in the same period.
- During the last 3 years, the Downside risk index is 17 , which is higher, thus worse than the value of 6.77 from the benchmark.

'Maximum drawdown measures the loss in any losing period during a fund’s investment record. It is defined as the percent retrenchment from a fund’s peak value to the fund’s valley value. The drawdown is in effect from the time the fund’s retrenchment begins until a new fund high is reached. The maximum drawdown encompasses both the period from the fund’s peak to the fund’s valley (length), and the time from the fund’s valley to a new fund high (recovery). It measures the largest percentage drawdown that has occurred in any fund’s data record.'

Which means for our asset as example:- Compared with the benchmark SPY (-33.7 days) in the period of the last 5 years, the maximum DrawDown of -63.1 days of ProShares Ultra Dow30 is lower, thus worse.
- Looking at maximum DrawDown in of -63.1 days in the period of the last 3 years, we see it is relatively smaller, thus worse in comparison to SPY (-33.7 days).

'The Maximum Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. It is the length of time the account was in the Max Drawdown. A Max Drawdown measures a retrenchment from when an equity curve reaches a new high. It’s the maximum an account lost during that retrenchment. This method is applied because a valley can’t be measured until a new high occurs. Once the new high is reached, the percentage change from the old high to the bottom of the largest trough is recorded.'

Using this definition on our asset we see for example:- Looking at the maximum days below previous high of 248 days in the last 5 years of ProShares Ultra Dow30, we see it is relatively larger, thus worse in comparison to the benchmark SPY (139 days)
- Compared with SPY (119 days) in the period of the last 3 years, the maximum time in days below previous high water mark of 248 days is higher, thus worse.

'The Average Drawdown Duration is an extension of the Maximum Drawdown. However, this metric does not explain the drawdown in dollars or percentages, rather in days, weeks, or months. The Avg Drawdown Duration is the average amount of time an investment has seen between peaks (equity highs), or in other terms the average of time under water of all drawdowns. So in contrast to the Maximum duration it does not measure only one drawdown event but calculates the average of all.'

Which means for our asset as example:- Compared with the benchmark SPY (35 days) in the period of the last 5 years, the average time in days below previous high water mark of 67 days of ProShares Ultra Dow30 is larger, thus worse.
- Compared with SPY (27 days) in the period of the last 3 years, the average days below previous high of 61 days is higher, thus worse.

Historical returns have been extended using synthetic data.
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- Note that yearly returns do not equal the sum of monthly returns due to compounding.
- Performance results of ProShares Ultra Dow30 are hypothetical, do not account for slippage, fees or taxes, and are based on backtesting, which has many inherent limitations, some of which are described in our Terms of Use.